Vulnerability in Scientific Theories without Popperian falsification

Popper held that falsifiability is what demarcates science from pseudoscience.  Pseudoscientific theories are compatible with all possible observation.  By contrast, scientific theories “stick their necks out”, where certain observations falsify the theory.

There have been various criticisms of Popper’s falsification criterion:

  • There is no distinction between observation and theoretical statements, because observation is theory laden.  Popper realized this.  He held that it was up to the scientific community to decide on what counted as observation statements.
  • If a statement S is falsifiable, we can conjoin any pseudoscientific statement P, so that S&P is falsifiable.  Presumably if P is not scientific, then S&P should not be either.  This is the tacking problem.
  • Popper’s falsification has the odd consequence that a statement can be scientific while the negation is not.  While “all swans are white” is falsifiable by the observation of a single non-white swan, the negation of that statement “there exists a swan that is non-white” is not falsifiable by finite observation.
  • As the Duhem-Quine thesis points out, all theories come with auxiliary theories.  In order to deductively falsify a theory, you need to verify the auxiliary hypotheses.
  • Probability statements are not, strictly speaking, falsifiable.  A fair coin is not necessarily falsified by 100 heads in a row.  Popper’s solution was to say that scientists were to specify, in their own fields, how improbable a result must be for a theory to be falsified.

Popper’s falsification criterion makes theories vulnerable, but it has the criticisms mentioned.  We want theories to be vulnerable to observation.  Theories could not do explanatory work if they were consistent with every possible observation.  Elliott Sober proposes an alternative to Popperian falsification that maintains the scientific virtue of vulnerability; and it follows from the Likelihood Principle.

Likelihood Principle: O strongly favors H1 over H2 if and only if P(O|H1) >> P(O|H2)

The likelihood P(O|H) is not to be confused with the probability P(H|O).  Suppose O is “there is a noise in the attic”, and H is “there are gremlins bowling in the attic.”  While P(O|H) is high, P(H|O) is low.  It would be strange to say that we should believe gremlins are in the attic because the likelihood is high.  The likelihood, by itself, does not tell you which hypothesis is more plausible.  It simply tells you that the observation favors one hypothesis over the other.  The plausibility of the hypothesis will be a function of the likelihood and the antecedent plausibility.

So how can the Likelihood Principle make theories vulnerable?  If P(O|H1) > P(O|H2), then P(not-O|H1) < P(not-O|H2).  This is derived from that fact that P(O|H1) + P(not-O|H1) = 1.  In other words, if O favors H1 over H2, then not-O favors H2 over H1, hence the vulnerability.   For Sober, testing is contrastive: testing a hypothesis means testing it against another hypothesis.

Sober, Elliott. Philosophy of Biology.

Sober, Elliott. Testability.

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10 Responses to Vulnerability in Scientific Theories without Popperian falsification

  1. Destructivist says:

    “As the Duhem-Quine thesis points out, all theories come with auxiliary theories. In order to deductively falsify a theory, you need to verify the auxiliary hypotheses.”

    Well, no. Verification (i.e. the mythical process whereby an idea or statement gets revealed to be true by the act of observation, experimentation, or whatever) plays no part in Popper’s philosophy. Popper was a thoroughgoing fallibilist, which means he denied that any such revelation of the truth was possible. So you’ve definitely misinterpreted him if you think this is a good criticism.

    It’s also worth mentioning that Popper didn’t think that a falsification revealed that a theory was false, either. Fallibilism doesn’t let you believe that truth OR falsehood can be ‘revealed’, or be manifest. We can only *guess*, tentatively, that some of our ideas are true or false.

    Perhaps a better way to look at it, is that combining some theories (an observation, some theory we’re interested in, and background theories) results in a logical incompatibility that has to be dealt with; a problem.

    This raises the question “What should we change or throw out to get rid of the problem?” Usually what we do before making a decision is turn a critical eye to all of the ideas in the combination. In science, theories have to be independently testable, meaning that they must explain some target fact they were originally constructed to explain, AND some other stuff. This makes debugging our ideas easier. So we go back and check all the ideas in the combo, and if we see a problem, we get rid of that idea, and hopefully that fixes everything, and the new combo no longer suffers from an internal logical inconsistency.

    If we can’t find any problems with our background theories, nor the observation, nor the theory we’re interested in, then we just have an open problem. There are lots of open problems in science, so Popperian philosophy of science isn’t deficient by allowing them.

    I may or may not comment on some of the other criticisms in your blog post, depending on how much available time I have, and how lazy I’m feeling. I figure it’s best to counter-criticize one thing at a time, at any rate.

    • I’m not saying Popper believed in confirmation. I’m aware of his use of corroboration and verisimilitude. The point is that the deductive relation only holds if the auxiliary hypotheses are verified. But you point out that Popper didn’t think we could conclusively say a theory was false.

      I didn’t explain the idea in detail in my post, but in Elliott Sober’s “Philosophy of Biology” page 50-51, this particular criticism is aimed at Popper’s asymmetry thesis between falsification and verification. The idea is that the asymmetry is gone once you involve auxiliary hypotheses. But you would probably deny that the auxiliary hypotheses are verified in the sense that we could be confident in them.

      With regards to verification or confirmation as opposed to corroboration, I take verification to be something like a boost in confidence (probably through induction) in that theory. If corroboration isn’t this, then how does Popper choose an untested theory over a tested one? This criticism is spelled out in better detail in Peter Godfrey-Smith’s “Theory and Reality” page 67-69.

      As an aside, according to Sober, most theories are independently testable, but some are not. For example,Reichenbach (1958) argued that hypotheses about the geometry of physical space and hypotheses about physical forces cannot be tested independently.

  2. Destructivist says:

    “The point is that the deductive relation only holds if the auxiliary hypotheses are verified. […] The idea is that the asymmetry is gone once you involve auxiliary hypotheses.”

    Popper’s position was that the whole system was falsified by the observation. Page 76 of The Logic of Scientific Discovery:

    “By means of this mode of inference we falsify the whole system (the theory as well as the initial conditions) which was required for the deduction of the statement p, i.e. of the falsified statement.”

    So instead of Sober’s argument form (If T&A, then P. A. ¬P. Therefore, ¬T.), you have: If T&A, then P. ¬P. Therefore ¬T&A. This is deductively valid. By contrast, “If T&A, then P. P. Therefore, T&A.” is not valid.

    T&A represent a system that is only falsifiable (not verifiable) by basic statements. So the asymmetry is preserved.

    “…you would probably deny that the auxiliary hypotheses are verified in the sense that we could be confident in them.”

    I would say that the auxiliary hypotheses, A, have the same status as the theory T in the above arguments. I would deny that they are verified in the sense that they can be deduced from a basic statement.

    If an idea (or system of ideas) has no criticism, then I think it’s fine to feel some confidence. I don’t see what it could hurt. If the confidence gets in the way of criticizing an idea that ought to be criticized, it’s bad. Tentative confidence is OK, though. But we’re talking about psychology now, and have left the realm of logic and epistemology.

    “If corroboration isn’t this [a boost in confidence], then how does Popper choose an untested theory over a tested one?” (bracketed text added)

    Are you asking “How does Popper avoid choosing untested theories over well-tested theories if the latter’s predictive successes count for nothing?”?

    If so, then my answer is: I don’t know that he does avoid choosing them. Maybe he does. I don’t know enough about Popper’s position to comment.

    I can tell you *my* position, or the positions of some people that have taken up the torch of Popper’s critical brand of philosophy and gone further, though.

    I do not think that using an untested theory is necessarily bad. Imagine that Einstein had never lived, and we still used Newtonian theory. There would be lots of observations that would be inconsistent with it by now. We’d know it’s wrong, but we’d have nothing to replace it with. Suppose that someone independently comes up with Einstein’s theory today. It would immediately explain all that Newton’s theory explains, AND all the problematic observations. But since the theory is brand new, we haven’t had time to test it yet. I say: So what? It was BORN good. We’d obviously want to test it, but it’s already a good theory because it accounts for more than any other we had previously.

    “For example,Reichenbach (1958) argued that hypotheses about the geometry of physical space and hypotheses about physical forces cannot be tested independently.”

    I’m not familiar with that argument. I’ll have to look it up.

    • “we falsify the whole system (the theory as well as the initial conditions)”

      I think the initial conditions would be the observation statement or a singular statement. Auxiliary hypotheses can be universal statements. If initial conditions are singular statements then the issue of auxiliary hypotheses is still open. If initial conditions include Quine’s whole web, when we say a theory is false, we’re really saying our entire belief set is inconsistent. Auxiliary hypotheses are infinite: the result of this experiment will not be affected by the color of my lab coat is an auxiliary hypothesis.

      “Tentative confidence is OK, though. But we’re talking about psychology now, and have left the realm of logic and epistemology.”

      I wouldn’t say we’ve left epistemology, but, in any case, confidence is why we choose to build a bridge out of tested theories over untested theories.

      “Suppose that someone independently comes up with Einstein’s theory today. It would immediately explain all that Newton’s theory explains, AND all the problematic observations”

      It seems like if it explained stuff explained by Newton’s theory and problematic observations, then it would be tested (by “old evidence” in the bayesian literature.) It would be untested in the sense that it hasn’t been tested with new evidence or with its novel predictions.

      On another note, when a scientist comes up with a new hypothesis (context of discovery), I don’t see how induction can be avoided. I think to much would be lost if we were to ignore induction altogether.

  3. Destructivist says:

    “I think the initial conditions would be the observation statement or a singular statement. Auxiliary hypotheses can be universal statements.”

    If you look at the context of that quote, you’ll find that Popper was lumping auxiliary hypotheses in with singular statements. From the previous paragraph on page 76:

    “Let p be a conclusion of a system t of statements which may consist of theories and initial conditions (for the sake of simplicity I will not distinguish between them).”

    Popper makes other remarks elsewhere in the book that indicate he regarded auxiliary hypotheses as being components within a system that is falsified. Page 83, for instance:

    “The introduction of an auxiliary hypothesis should always be regarded as an attempt to construct a new system”

    His position shouldn’t be confused with that of Quine’s, though. He isn’t saying that our entire theoretical web gets falsified. He says that only the subsystem that is required for the derivation of a prediction gets falsified. So the damage done by the acceptance of a basic statement can be very limited.

    “It seems like if it explained stuff explained by Newton’s theory and problematic observations, then it would be tested (by “old evidence” in the Bayesian literature.) It would be untested in the sense that it hasn’t been tested with new evidence or with its novel predictions.”

    If that’s what you want ‘tested’ to mean, then all ‘live’ theories in science were already well-tested at the time of their birth. If they explain anything, they explain ‘old evidence’. Since that old evidence didn’t falsify them, you’d say they were born having already passed many tests.

    I’ll rephrase my position (which may be Popper’s too): I don’t think it’s bad to use a new theory that is untested in the sense that its novel predictions haven’t been tested by new evidence. The very fact that it explains more than its predecessors and rivals makes it better than them.

    We should definitely get around to testing those novel predictions, though.

    “On another note, when a scientist comes up with a new hypothesis (context of discovery), I don’t see how induction can be avoided. I think too much would be lost if we were to ignore induction altogether.”

    I disagree. I hold Popper’s position, which is that induction is a mythical process that nobody actually uses, analogous to other mythical idea-generating processes, like divine revelation. But that’s a topic for another thread. I just wanted to address a misconception that Elliot Sober has, which you put on your blog.

  4. Destructivist says:

    “There is no distinction between observation and theoretical statements, because observation is theory laden. Popper realized this. He held that it was up to the scientific community to decide on what counted as observation statements.”

    To my knowledge, Popper laid out various criteria that an observation-statement (i.e. basic statement) must meet. It’s our decision whether we’ll identify basic statements as the test-statements of science.

    Anyway, just because observations contain theoretical terms doesn’t mean they can’t be distinguished from other kinds of theoretical statements.

    An observation statement specifies what *does* happen in a *finite spatiotemporal region in a particular world*.

    A universal statement specifies what *doesn’t* happen *anywhere, at any time, in any world*.

  5. Destructivist says:

    “If a statement S is falsifiable, we can conjoin any pseudoscientific statement P, so that S&P is falsifiable. Presumably if P is not scientific, then S&P should not be either. This is the tacking problem.”

    I’m going to rephrase this criticism in a way that eliminates charged words like ‘pseudoscientific’, because I’d like to look at it in a more sterile and objective light:

    “If a statement (or system of statements) S is falsifiable, we can add to it an explanationless assertion P, so that S&P is falsifiable. Presumably if P is unfalsifiable, then S&P should not be either.”

    I just don’t see why S&P ought not be falsifiable, though. What kind of intuition is being violated by accepting that S&P are falsifiable? It’s not clear to me why this represents a problem in and of itself. It’s just a matter of logic.

    We’re not in danger of taking P seriously, if that’s the worry. I’ll quote Popper from page 83 of The Logic of Scientific Discovery:

    “As regards auxiliary hypotheses we propose to lay down the rule that only those are acceptable whose introduction does not diminish the degree of falsifiability or testability of the system in question, but, on the contrary, increases it.”

    This doesn’t just apply to auxiliary hypotheses. If we want to add an assertion (such as P) to our system of falsifiable statements, P must serve to increase the falsifiability of that system, per Popper’s methodological rule. Clearly, a pseudoscientific assertion can’t do that, so it’s not allowed to join the club, so to speak.

    Most people that encounter this methodological rule are going to wonder why they ought to accept it. It seems like Popper just pulled it out of his ass and told us “This is how good scientists should behave”.

    An advocate of Popper’s ideas named David Deutsch explains why this methodological rule should be accepted on pages 65-66 of his book The Fabric of Reality (apologies for the wall of text to follow, which I had to type out by hand):

    “If a theory about observable events is untestable – that is, if no possible observation would rule it out – then it cannot by itself explain why those events happen in the way they are observed to and not in some other way. For example, the ‘angel’ theory of planetary motion is untestable because no matter how planets moved, that motion could be attributed to angels; therefore the angel theory cannot explain the particular motions that we see unless it is supplemented by an independent theory of how angels move. That is why there is a methodological rule in science which says that once an experimentally testable theory has passed the appropriate tests, any *less* testable rival theories about the same phenomena are summarily rejected, for their explanations are bound to be inferior. This rule is often cited as distinguishing science from other types of knowledge-creation. But if we take the view that science is about explanations, we see that this rule is really a special case of something that applies naturally to all problem-solving: *theories that are capable of giving more detailed explanations are automatically preferred*. They are preferred for two reasons. One is that a theory that ‘sticks its neck out’ by being more specific about more phenomena opens itself up to more forms of criticism, and therefore has more chance of taking the problem-solving process forward. The second is simply that, if such a theory survives criticism, it leaves less unexplained – which is the object of the exercise.” (text enclosed by asterisks is italicized)

    The last sentence is the most important for my point. Whenever we want to add a statement to our system, we have to ask: Does it solve any problem, or does it only create a problem? Accepting pseudoscientific statements invariably creates explanatory problems. We immediately want to know how the posited entities interact with observable stuff, and what rules they obey. Since pseudoscientific theories never answer those kinds of questions, they are bad explanations, and leave us hanging with unnecessary open problems. So they have to go.

  6. I think you’re right about the asymmetry of the “whole system.” I asked Sober and here’s what he has to say:

    “If one wants to show that T is falsifiable, it is a change in subject to show that T&A is falsifiable.

    Popper famously claimed that Marxism and Fruedianism are unfalsifiable, but doesn’t consider that Marx&A1 or Freud&A2 might be falsifiable. Ditto for the quesiton of whether “God exists” is falsifiable.

    Having said that, I agree that Popper can get an asymmetry between verifiability and falsifiability for SOME propositions.”

    As far as the tacking problem (and other problems), I don’t consider it to really be a problem. It’s an issue that has been noticed by the logical positivists.

    • Destructivist says:

      “If one wants to show that T is falsifiable, it is a change in subject to show that T&A is falsifiable.”

      I think what Elliot is saying here, is “If you want to isolate T as being the cause of the falsification, it’s a non sequitur to show that T&A can be falsified.”

      But sometimes you just *can’t* show that T is to blame, because you have no independent reasons for rejecting T, A, or ¬O. So all you can do is say that T&A are incompatible with the observation.

      Sometimes, no criticism will be found for A, nor ¬O, but one will be found for T. In that case, T is refuted. That’s not the same as saying that A (or ¬O) is verified by observations, though. A is merely unrefuted (so far) by our observations, and has the status ‘OK’.

  7. To critique the tacking problem charitably, it is assumed that the problem refers to conjunctions only of propositions forming valid arguments, because a proposition that is neither true nor false is not a falsifiable proposition such that a conjunction can be falsifiable and, therein, can be true/false only if of all of its conjoined propositions form a valid argument. Any pair of propositions is a valid argument if their pair forms a valid syllogism. Thus, an unfalsifiable conjunction is formed by a proposition that is falsifiable and one that is not if they form an invalid argument. There is no ‘tacking problem’ for Popperian falsificationism because it is a priori false that a falsifiable proposition and an unfalsifiable proposition can form a falsifiable conjunction and, in attempting to defend the ‘tacking problem’ argument from the following counterargument, up to four counts of fallacious argumentation can result.

    I. FALSE CRITICISM
    “A falsifiable proposition and an unfalsifiable proposition can form a falsifiable conjunction” is an a priori false proposition. The conjunction of a falsifiable proposition and an unfalsifiable proposition can be a falsifiable conjunction only if the two conjoined propositions form a valid argument, and if such is not possible then a falsifiable proposition and an unfalsifiable proposition cannot be a falsifiable conjunction. No falsifiable conclusion from the argument of any valid syllogism can be formed with one premise that is falsifiable and the other that is not because the middle term of any syllogism with such premises cannot be a predicate that makes any proposition (of which it is the predicate) an unfalsifiable proposition.

    II. FALLACIOUS ARGUMENTATION
    Not to mention the obvious moving of the goalposts, up to four counts of fallacious argumentation can result in attempting to defend the tacking problem argument. In attempting to defend it, three of the counts of fallacious argumentation can result from making an argument from analogy (of logical operations on propositions & predicates with mathematical operations on the real numbers).

    (II.1) False analogy
    ‘An a posteriori falsifiable proposition IS TO a negative real number AS
    an a posteriori unfalsifiable proposition IS TO a positive real number.’
    This argument from analogy is a priori false because, to a marginal degree, the unary logical operation of negation is more similar to the mathematical operation of the unary negative than it is to the unary positive. Unlike elements operated on by the unary positive, if elements are not operated on by negation or the unary negative an even number of times then the operations are not neutral; multiplying two negative real numbers cancels the unary negative of each real number quite like the double negation of a proposition or predicate cancels a single negation of the proposition or predicate.

    (II.2) False equivalence
    ‘An a posteriori falsifiable proposition IS TO a positive real number AS
    an a posteriori unfalsifiable proposition IS TO a negative real number.’
    This argument from analogy asserts an a priori false equivalence between the unary logical operation of negation and the mathematical operation of the unary negative, which are not equivalent. ‘Negative three’ necessarily is ‘not three’ but ‘not three’ is not necessarily ‘negative three’ (because one, two, four, etc., for example, also are ‘not three’), however ‘unfalsifiable’ always is the negation of ‘falsifiable.’ The unary logical operation of negation and the mathematical operation of the unary negative are not equivalent because, whereas the unary negative operates on the natural numbers to produce a set of additive inverses of all of the natural numbers, negation is a unary logical connective that operates on the existential quantifier of a proposition or predicate.

    (II.3) False exclusionary disjunct
    ‘What is a posteriori falsifiable IS TO what is a posteriori unfalsifiable AS
    a real number IS TO the additive inverse of that real number.’
    This argument from analogy falsely excludes a disjunct because, whereas only one logically possible predicate can be the negation of another predicate, the negation of the additive inverse of a real number can imply not only a positive or a negative real number but also a real number that is neither only positive nor only negative (e.g. the additive inverse of zero is neither positive nor negative on the unextended real number line). The false exclusionary disjunct of this argument equivocates the binary logical operation of conjunction with the unary logical operation of negation and, thus, it falsely is excluded that, perhaps, if a predicate and its negation are the only two predicates of the only two propositions of a conjunction then neither of their predicates is equivalent to the conjunction’s predicate. Thus, the possibility is falsely excluded that a falsifiable proposition and an unfalsifiable proposition can be a conjunction that is neither falsifiable nor unfalsifiable. It is possible that a conjunction of a true proposition and a false proposition is neither a true nor a false proposition. For example, “this is a complete sentence and this sentence is false” is a proposition that posits the following paradoxical belief: this complete sentence is false. Provided that the conjunction is grammatical, a sentence that is expressed in realis mood and another that is expressed in irrealis mood can express both realis mood and irrealis mood as a conjunction. For example, “I want you to help me lift this, but don’t feel pressured to do so” first expresses realis mood and then expresses irrealis mood. Additive inverses of the imaginary unit, signed infinity, signed zero, and every real number sum to a real number that is neither a positive number nor a negative number.

    (II.4) Illicit transference
    Reasoning that the conjunction of a falsifiable proposition and an unfalsifiable proposition can be falsifiable on the basis that one of the propositions is falsifiable is the fallacy of composition because such an argument relies on the assumption that the conjunction and at least one of the conjoined propositions have a symmetric relation of their predicates under a strict partial order, which is an assumption that illicitly transfers predication from one of the two proper parts of the non-atomic proposition to the non-atomic proposition. An argument implying wholly from the predicates of two propositions anything about the predicate of their conjunction illicitly transfers predication because, whereas the unary logical connective of negation operates on the existential quantifier, conjunction is a binary logical connective that operates on no quantifier at all such that the logical relationship of the conjunction to the conjoined necessarily is qualitative (and contingently is quantitative).

    https://www.academia.edu/28528343/In_Defense_of_Popperian_Falsificationism_from_Attack_by_the_Tacking_Problem_Argument

    Another criticism of the falsification principle of the Popperian philosophy of science is: that the negation of an a posteriori falsifiable proposition can be unfalsifiable suggests that an a posteriori falsifiable, objectively true/false, universally quantified proposition is not necessarily a scientific proposition. Invoking this observation as the basis for criticism of Popperian falsification amounts to the suggestion that science ought to ignore facts and, unwittingly (and ironically), serves to highlight a key strength of the falsification principle of the Popperian philosophy of science.

    I. An a posteriori unfalsifiable proposition that is a posteriori falsifiable upon its negation is logically distinct from an a posteriori unfalsifiable proposition that is a posteriori unfalsifiable upon negation.

    II. Misbelieving that any randomly selected false proposition is a true proposition is riskier if the selected proposition is of a class of propositions that are equiprobably true/false than it is if the selected proposition is not of such a class because:
    – II.1 – There is a greater possible chance for an a posteriori falsifiable proposition to be proven a posteriori objectively false than to be proven a posteriori objectively true.
    – II.2 – The risk that is associated with a class of unfalsifiable propositions is indifferent to all new facts, knowledge, observation, information, evidence and the like.

    III. If an a posteriori unfalsifiable objectively true proposition is the truthmaker of an a posteriori falsifiable objectively false universally quantified proposition then a fact is the truthmaker of the a posteriori unfalsifiable objectively true proposition. For example, if “some swans are not white” is true due to the fact that at least one swan presently is not white, then it makes “all swans are white” false, which makes “not all swans are white” true.

    An a posteriori falsifiable universally quantified proposition often is objectively false whilst its unfalsifiable negation is objectively true. Rather than a paradox, this is an emblem of the cumulative character of learning. It is of that which bestows epistemic potency upon any kernel of theoretical power.

    https://www.academia.edu/28415549/In_Defense_of_Popperian_Falsification_from_Attack_by_the_Negation_Problem_Argument

    ~~
    Aaron Henriquez Rubin
    רובין אהרן
    https://www.facebook.com/ahrubin
    https://independent.academia.edu/AaronHRubin

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